Learn Quadratic Equations Visually

MULTIMEDIA KIT DOCUMENT 1

Multimedia Kit Document

Devon Kinne

CIMT 543

Summer 2012

Dr. Ziaeehezarjeribi

Indiana State University


Multimedia Kit Document

Students today look to instruction and the curriculum as something that, in order to help

them learn, must be engaging and multi-modal. Throughout all the facets of their life, students

use technology and media in order to learn. Some of these media include traditional textbooks,

video, podcasts, and manipulatives. Smaldino, Lowther, and Russell (2012) state that using a

variety of media such as video can “take the learner almost anywhere and extend students‟

interests beyond the walls of the classroom” (p.234). By engaging students with not only the

traditional text-based curriculum but also audio and video technology, student‟s learning can be

expanded in four of the major learning domains: cognitive, affective, psychomotor, and

interpersonal (Smaldino, Lowther, & Russell, 2012, p.235). This also helps to meet the needs of

many kinds of diverse learners, including those with hearing impairment, those who may need

more time for processing of oral information, as well as with gifted students (Smaldino et al.,

2012). This multimedia kit uses a variety of media, including traditional media such as

manipulatives, in order to attempt to keep students engaged and involved in the learning process.

Concept Map

The concept map below was created using the Inspiration 9 Concept Map software. In

the concept map, the two main concepts and three sub-concepts are displayed, along with their

connection to the components from the multimedia kit.


Concept Map Outline

Quadratic Equations

1. Concept: Parabolas Around Us

A. Images Found By Students

i. Resources:


1. Teacher created rubric – Parabolas Around Us:

http://parabolasaroundus.weebly.com/power-point-rubric.html

2. Teacher created Interactive Quiz:

http://www.thatquiz.org/tq/classtest?LEUF2928

3. Teacher created PowerPoint – Linear Equations All Around Us:

https://www.dropbox.com/s/ohpjydb9zwfp83n/LinearEquationPres

entation.wmv

B. Hanging String

i. Resources

1. Teacher created video: Determining the Equation of a Parabola

2. Website – Interactive Parabolas:

http://www.mathwarehouse.com/quadratic/parabola/interactive-

parabola.php

3. Manipulatives – string and tape

2. Concept: Interpolating Points

A. Concept: Solving Systems of Equations

i. Resources

1. Teacher created PowerPoint – Linear Equations All Around Us:

https://www.dropbox.com/s/ohpjydb9zwfp83n/LinearEquationPres

entation.wmv

2. Teacher created PowerPoint - Quadratic Equations: Systems and

Graphs -


https://www.dropbox.com/s/kiaumcum165xvwg/DevonKinneCIM

T543Summer2012VIsualPrinciples.pptx


Multimedia Kit
Target The learners are students at East High School in Madison, Wisconsin. There are
Learners
26 students in the class; 10 females and 16 males. Since this is an Algebra 2

course, the students are primarily either sophomores or juniors in high school.

The students who are sophomores are on-track to take AP Calculus their senior

year; the junior students are on-track to take Pre-Calculus their senior year.

There are 8 sophomores and 18 juniors. Three students in the class have

disabilities documented in an individualized education plan (IEP). None of

these students receive extra support services in class; one student is permitted

extra time on exams. Data regarding free/reduced lunch is not available for the

specific class; however, 58% of the school in total is eligible for free/reduced

lunch (Madison Metropolitan School District, 2012). There are 17 Caucasian

students, 1 Middle Eastern student, three Black students, 2 Hispanic students,

and 3 Asian students. The students all enjoy using technology during the class

time and tend to react enthusiastically when presented with assignments that

require the use of technology, especially presentations.

Learning Students will substitute points on a graph into a function form to find the
Objectives:
equation of a graph correctly 80% of the time.

Students will graph quadratic equations on their graphing calculator, choosing

an appropriate window to view the graph, 80% of the time.

Students will explain the difference between quadratic and linear functions,

both by their graphs and their equations, 80% of the time.


Students will take a picture with a digital camera of a parabolic function found

in nature or architecture.

Students will make real-world connections, recognizing shapes around them

that can be approximated by quadratic equations, 80% of the time.

Students will create a presentation using PowerPoint and score 20/24 or higher

on the teacher created "Parabolas Around Us" Power Point Rubric.

Students will take an online interactive quiz and score a 35/44, or 80%, or

higher.

Components This lesson teaches students about quadratic equations; specifically, the
of the Kit
relationship between a parabolic graph and the corresponding quadratic

equation. Students will learn how to solve systems of equations, in order to

interpolate points from a parabola into a representative quadratic equation. This

topic was chosen due to the struggles that many students have with traditional

methods of instruction on this topic. Smaldino, Lowther, and Russell (2012)

report that using a variety of media “can make your lesson more realistic and

engaging” (p.256), which will help students to engage in the material and grasp

the material more fully.

Learning Resources:

1. Teacher created “Quadratic Equations – Systems and Graphs”

PowerPoint (includes images, graphs, and text): This resource is


originally my “Visual Principles” assignment. This PowerPoint

discusses and demonstrates, in detail, the relationship between points on

a parabola and the creation of a quadratic equation representation. It

focuses on the mathematical algorithm for solving systems of equations,

and gives step-by-step examples for students to follow along with. This

PowerPoint includes a variety of images and graphs which will be

modeled and reused in other resources of the Multimedia Kit, providing

consistency and will spark recognition of the topic.

2. Teacher created video – “Determining the Equation of a Parabola”: This

resource was created as my “video” assignment. In this video, students

will take the knowledge that they learned about solving systems of

equations and interpolation points, and bring it into the real world by

exploring the parabolic shape that naturally occurs when you hang a

string by two endpoints. Students will learn how they can take an object

that they see around them (for instance, a chain hanging to block off an

exhibit) and be able to interpolate points from it to create the quadratic

equation.

3. Interactive website – “Interactive Parabolas” -

http://www.mathwarehouse.com/quadratic/parabola/interactive-

parabola.php

4. Manipulatives – string, tape, and graph paper/whiteboard: While

something simple such as string and tape might be viewed curiously as a

resource in a multimedia kit, the use of manipulatives like these often


“attract students attention and promote learning because the students can

handle and inspect them” (Smaldino et al., 2012, p.263). The use of

string, tape, and graph paper/white board allows for students to

manipulate a parabola directly in their hand, and explore how the

changes in shape relate to the changes in coefficients a, b, and c, of the

quadratic equation. Combined with Resource #3, students will continue

to experiment in a hands-on manner to make a direct connection

between the relationship of a parabola and its corresponding equation.

As Smaldino et al. (2012) state, real objects, such as the hanging banner

that creates a parabola, are some of the most “intriguing and involving

materials in educational use” (p.263).

5. Teacher created “Linear Equations All Around Us” PowerPoint

(includes images, audio, graphs, and text): This PowerPoint presentation

serves as an example for students to experience what their final

PowerPoint presentation should look like. This will serve as a reminder

of various elements that must be present for their final presentation,

such as the use of their images as well as the corresponding equations

and graphs that they calculated.

Assessment Tools:

1. Teacher created “Quadratic Equations in Nature” PowerPoint rubric

(Appendix 1). Following the exploration of quadratic equations and

parabolas, both through the mathematical solving of systems of

equations and interpolation and through exploring the world around


them to discover parabolas in nature, the students will then create a

PowerPoint presentation. This presentation is part of the “Require

Learner Participation” section of the ASSURE lesson plan. The

students will be able to refer to Resource 5 above to see an example of a

similar PowerPoint presentation focusing on linear equations. As

students work, they can be referring to this rubric to maintain their

focus. This form of “authentic assessment” focuses not simply on the

end result, but the processes and skills that the students learned in the

project (Smaldino et al., 2012, p.55). The PowerPoint rubric will be

used to grade their presentations, focusing on the digital images they

took, audio explanation, and graphical interpretation. Students will also

complete a worksheet and self-score themselves, providing immediate

feedback, to determine if they got the 80% needed to demonstrate

satisfactory performance.

2. Teacher created Interactive Quiz, located at

http://www.thatquiz.org/tq/classtest?LEUF2928. This is the last

component of the multimedia kit, and can be used by students to assess

a complete understanding of the mathematical material they learned in

this lesson. Each student will take the quiz independently. This quiz

takes a long time to complete and should expect to take a full class

period to work on it. There are 44 possible points on this quiz; in order

to receive credit, students must score a minimum of 80%, or 35 points.

Students will be instructed to write their work down when doing the


problems, indicating which problems they got correct originally. The

Interactive quiz allows students to go back and see incorrect work.

Students may make changes to their problems, as long as they show all

of their work and indicate their mistakes. Students may make as many

corrections as they need to get a minimum of 80%; they may also

continue to make corrections and show their work and receive a higher

score. Since the process is required to earn points, students cannot

simply write the answer down but must have truly understood the

material enough to make changes and see their mistakes. I have chosen

this form of assessment, which is similar to a traditional test but allows

for improvement, with hopes that it will curb some test-taking anxiety

that many high school students face. The whole process is being

assessed, rather than simply the end result.

Instructional A variety of teacher-centered and student-centered strategies will be employed
Strategies
and Rationale in this lesson. Teacher-centered strategies will be used to teach the students the

actual mathematical algorithms that are needed to solve systems of equations

interpolate points to create and equation. These are two topics that students

often struggle with; without direct, teacher-centered strategies, such as the

PowerPoint presentation in resource 1and the video in resource 2, students

would likely struggle with the algorithmic thinking necessary to complete the

rest of the project. Resource 1 and 5 demonstrate, via a presentation, how to

solve a system of equations and interpolate points to a parabola. This lends


itself nicely to teacher-centered strategies, where “the teachers are the „drivers‟

who direct the learning in very purposeful ways” (Smaldino et al., 2012, p. 70).

This teaching is done numerous times in both resources, with many examples,

so that students will gain a strong foundation to apply their knowledge to their

own future explorations.

The majority of the other learning will take place through student-centered

strategies. Student-centered strategies have been shown to enhance learning

“when students are actively engaged in meaningful activities” (Smaldino et al.,

2012, p.72). Students will be given a variety of different graphs and equations

to experiment with, in order to try to come up with an algorithm for

interpolation. Students will use manipulatives, such as strings, in order to create

parabolas and then hypothesize equations that fit these models. Students will be

given various resources, such as Resource 3 and Resource 4, where they can

experiment and hypothesize the relationship between the equation and the

parabola. Students will also be sent out to collect images via digital camera,

and then transpose those images onto graphs and come up with corresponding

equations. Lastly, students will collaborate with their partners to create their

PowerPoint presentation. The interactive quiz, in Assessment2, can then be

used to have students self-assess whether or not they understood the

mathematical concepts learned from each resource.


References

Kinne, D. (2012). Quadratic equations: Systems and graphs. Retrieved June 3, 2012, from

https://www.dropbox.com/s/kiaumcum165xvwg/DevonKinneCIMT543Summer2012VIs

ualPrinciples.pptx

Kinne, D. (2012). Parabolas around us webquest. Retrieved June 3, 2012, from

http://parabolasaroundus.weebly.com/

Madison Metropolitan School District. (2012). Official third Friday September enrollment by

low income. Retrieved May 19, 2012, from

https://infosvcweb.madison.k12.wi.us/node/989

Math Wearhouse. (2012). Interactive parabolas. Retrieved June 3, 2012, from

http://www.mathwarehouse.com/quadratic/parabola/interactive-parabola.php

Smaldino, S.E., Lowther, D.L., & Russell, J.D. (2012). Instructional technology and media for

learning(10th ed.). Boston, MA: Pearson Education, Inc.

Learn Quadratic Equations Visually

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